The U.S. Justice Department’s lawsuit accusing Fiat Chrysler Automobiles NV of using illegal software to cheat on emissions tests with diesel-powered vehicles is headed to a California court to join other widespread litigation against the auto maker, according to an order from a group of federal judges.

The U.S. Judicial Panel on Multidistrict Litigation on Wednesday ordered the Justice Department’s civil suit be transferred to a federal court in San Francisco to join ongoing proceedings stemming from similar allegations...